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Abstract

We present a method for recording in-line single-shot digital holograms based on the fractional Talbot effect. In our system, an image sensor records the interference between the light field scattered by the object and a properly codified parallel reference beam. A simple binary two-dimensional periodic grating is used to codify the reference beam generating a periodic three-step phase distribution over the sensor plane by fractional Talbot effect. This provides a method to perform single-shot phase-shifting interferometry at frame rates only limited by the sensor capabilities. Our technique is well adapted for dynamic wavefront sensing applications. Images of the object are digitally reconstructed from the digital hologram. Both computer simulations and experimental results are presented.

Figures (7)

Schematic diagram of the phase distribution at the 1/4 fractional Talbot plane provided by an amplitude 2D grating, and the corresponding irradiance distribution at the 1/2 Talbot plane. The magnified unit cell shows the different phases obtained at the 1/4 Fresnel image.

Pictures of the irradiance distribution associated to the input 2D objects located at the object beam of the optical system depicted in Fig. 3. Objects (a) and (b) are assumed to be at a distance z1 = 400mm and z2 = 300 mm from the CCD sensor, respectively.

Gray level pictures corresponding to the results of the numerical simulation: (a) Talbot interferogram at the output plane of the optical system in Fig. 1, (b) and (c) reconstructed images at two different distances from the resulting digital hologram. The Fresnel image projected onto the sensor plane corresponds to that obtained at a distance from the grating given by (1 + 3/4)zt.

Gray level pictures of a central region of the light distribution generated by the grating at the output plane of the system in Fig. 1: (a) Irradiance distribution of the first self image, (b) uniform irradiance distribution of the Fresnel image with z´ = (1 + 3/4)zt, (c) interference pattern between the same Fresnel image and a parallel object beam showing the periodic three-step phase distribution.

Gray-level pictures of a partial region of the interference patterns generated at the output plane of the Talbot holography system in Fig. 1 for different 2D objects located at the object beam: (a) the object in Fig. 3(a) and (b) the object in Fig. 3(b). The grating located at the reference beam generates the Fresnel image corresponding to z´ = (1 + 3/4)zt. Note the pixelated structure.

Gray level pictures showing the result of the reconstruction of the different digital holograms recorded experimentally: (a), (b), and (c) show the reconstruction of the objects in Fig. 3(a), Fig. 3(b) and the USAF resolution target, respectively.